FRACTARIUM Interactive Observatory for Mathematical and Emergent Phenomena
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OBSERVATION CHAMBER / MVP

Symmetry Copy Maker

Choose rotations or reflections and watch copies orbit around axes and fixed points.

symmetry Operational

SYMMETRY FIELD

Drag a seed point and watch rotations, reflections, inversions, axes, and fixed centers copy it into a moving orbit.
OBSERVING
First observation Drag the bright seed point. AXIS shows mirror lines, FIXED highlights the unmoving center, and TRACE keeps a faint memory of the orbit.
ORBIT / AXIS / FIXED / TRACE
orbit 8 / axes 8
OBS-000 / ROTATION / 00:00

SYSTEM NOTE

Touch one point and the symmetry answers.

A visual symmetry-orbit model. Not a formal proof or algebra system.

OBSERVATION POINTS

Copies, axes, and fixed centers.

  • Rotation keeps the orbit clean and circular.
  • Reflection and Dihedral make mirror axes readable.
  • Kaleido lets small offsets show where symmetry begins to wobble.

OBSERVATION GUIDE

Touchpoints for Observation

Observe one seed point spreading into symmetry copies through rotations, reflections, inversions, mirror axes, and fixed centers.

  • Drag the seed, switch Rotation, Reflection, Dihedral, Inversion, or Kaleido, then compare ORBIT, AXIS, FIXED, and TRACE lenses.
  • ORDER changes how many copies appear around the center.
  • AXIS and FIXED views make the underlying symmetry easier to read.
  • Kaleido keeps the motion visual without turning it into a proof system.

This is a visual symmetry-orbit model, not a formal proof or algebra system.

Runs inside the browser with no upload and no registration.

SYSTEM NOTE

orbit(x) = {g.x | g in G}. Repeated rotations, reflections, and inversions copy one seed into visible orbits, axes, and fixed points.

OBSERVATION POLICY

This observation LAB runs in your browser. It does not upload images, pointer traces, or input.

Continue observation through connected systems.

FRACTAL Fractal Zoomer Space / Recursive Structure CHAOS Chaos Map Lab Time / Bifurcation FIELD Flow Field Painter Flow / Field WAVE Resonance Tuner Wave / Resonance NETWORK Slime Route Builder Network / Emergence ECOSYSTEM Ecosystem Balancer Life / Drift ORBIT Gravity Slingshot Orbit / Gravity DIMENSION 4D Shadow Projector Dimension / Projection CELL Cell Rule Playground Cell / Pattern EQUATION Equation Motion Engine Equation / Motion BRANCH Decision Collapse Tree Branch / Collapse COMPLEX Complex Function Warper Complex / Mapping PROJECTION Sphere-to-Plane Mapper Projection / Sphere HYPERBOLIC Infinite Tile Disk Hyperbolic / Tiling ECHO Mutation Chain Lab Echo / Inheritance SWARM Swarm Rule Mixer Swarm / Emergence INK Ink Plume Tank Ink / Diffusion REACTION Pattern Chemistry Lab Reaction / Pattern GROWTH Particle Branch Builder Growth / Aggregation DISCHARGE Lightning Generator Discharge / Branching CRITICAL Avalanche Sandpile Criticality / Avalanche PULSE Pulse Route Network Signal / Pulse THRESHOLD Threshold Grid Threshold / Connectivity LENS Gravity Lens Warper Lens / Light KNOT Knot Crossing Inspector Knot / Invariant PHASE Phase Transition Furnace Phase / Order TERRITORY Territory Splitter Territory / Distance MAGNETIC Magnetic Field Sandbox Magnetic / Polarity
CURRENT Symmetry Copy Maker Symmetry / Orbit
INTERFERENCE Wave Interference Basin Wave / Interference GRAMMAR Rule-Grown Garden Grammar / Growth GAP Prime Gap Constellation Prime Gap / Density MODULAR Modular Domain Explorer Modular / Fundamental Domain RADON Projection Scanner Radon / Reconstruction CRYSTAL Crystal Growth Furnace Crystal / Growth VORTEX Vortex Flow Mixer Vortex / Flow NEURAL Neural Pulse Network Neural / Reroute IMMUNE Virus Defense Arena Immune / Defense RESISTANCE Flow Tank Lab Flow Tank / Wake FLOW Obstacle Flow Lab Grid Flow / Solid Mask FLOW Karman Vortex Tank Cylinder Wake / LBM FLOW CFD Solver Lab Pressure / Projection CANDIDATE AI Word Flow Words / Candidate Competition COMPLEX Riemann Sheet Navigator Complex Path / Monodromy SPECTRUM Spectral Drum Membrane / Eigenmodes TOPOLOGY Topology Flood Persistence / Connectivity OPTIMIZATION Optimal Transport Workbench Mass / Global Allocation MONODROMY Polynomial Root Braid Comparator Root Paths / Order STRUCTURE P-adic Lift Tree P-adic / Lift Tree GEOMETRY Elliptic Curve Group Law Elliptic Curve / Group Law STRUCTURE Lattice Reduction Forge Lattice / Basis HYPERBOLIC Hyperbolic Isometry Studio Hyperbolic / Isometry TROPICAL Tropical Curve Balancer Tropical / Balance HODGE Hodge Decomposition Workbench Cochain / Hodge TIME / SYNCHRONIZATION Temporal Entrainment Chamber Time / Synchronization CAUSALITY / LIGHT CONE Causal Cone Observatory Causality / Light Cone TIME / SYNCHRONIZATION Distributed Clock Network Time / Synchronization TIME / ALIASING Temporal Aliasing Observatory Time / Aliasing TIME / SYNCHRONIZATION Collective Synchronization Transition Field Time / Synchronization PROBABILITY / DIFFUSION Random Walk Diffusion Field Probability / Diffusion OPTICS / DISPERSION Prism Dispersion Observatory Optics / Dispersion LIGHT / TRANSPORT Radiance Cascade Light Transport Field Light / Transport GEOMETRY / FRACTAL VOLUME Sierpiński Tetrahedron Observatory Geometry / Fractal Volume FLOW / ADVECTION Volumetric Advection Field Flow / Advection GEOMETRY / HARMONICS Spherical Harmonic Surface Observatory Geometry / Harmonics WAVE / DISPERSION Spectral Wave Surface Field Wave / Dispersion DYNAMICS / PHASE SPACE Symplectic Map Phase-Space Observatory Phase Space / Area-Preserving Map GEOMETRY / CURVATURE Discrete Curvature Mesh Observatory Geometry / Curvature STRUCTURE / GRAPH DIFFUSION Graph Spectral Diffusion Field Graph / Diffusion STRUCTURE / DENSITY GEODESIC Optimal Transport Density Geodesic Observatory Density / Wasserstein Geodesic STRUCTURE / DIFFRACTION Quasicrystal Diffraction Observatory Quasicrystal / Diffraction SCALE / RENORMALIZATION GROUP Renormalization Flow Observatory Scale / Renormalization Group FIELD / EIKONAL WAVEFRONT Eikonal Geodesic Wavefront Observatory Field / Eikonal Wavefront QUANTUM / HOLONOMY Berry Phase Holonomy Observatory Quantum / Holonomy CRITICAL POINT / LEVEL SET Morse Landscape Observatory Critical Point / Level Set CATASTROPHE / EQUILIBRIA Catastrophe Surface Observatory Catastrophe / Equilibria NOETHER / CONSERVATION Noether Symmetry Conservation Observatory Noether / Conservation MODULAR / FAREY TESSELLATION Modular Geodesic Tessellation Observatory Modular / Farey Tessellation WAVE / NONLINEAR DISPERSION Soliton Scattering Field Wave / Nonlinear Dispersion STRUCTURE / RANDOM GRAPH Random Graph Giant Component Observatory Structure / Random Graph DEFECT / WINDING Topological Defect Winding Observatory Defect / Winding STRUCTURE / CATENARY EQUILIBRIUM Catenary Chain Observatory Static Equilibrium / Catenary STRUCTURE / CAPILLARY BALANCE Capillary Rise Observatory Surface Tension / Capillary Balance PARTICLE / TRACK VISIBILITY Cloud Chamber Track Observatory Particle / Track Visibility FIELD / PHOTOELASTIC STRESS Photoelastic Stress Observatory Field / Photoelastic Stress DYNAMICS / POINCARé SECTION Double Pendulum Poincaré Observatory Dynamics / Poincaré Section QUANTUM / TUNNELING Quantum Tunneling Observatory QUANTUM / TUNNELING GEOMETRY / MINIMAL SURFACE Catenoid Minimal Surface Observatory GEOMETRY / MINIMAL SURFACE LATTICE / BAND GAP Phononic Band Gap Observatory LATTICE / BAND GAP OPTICS / DIFFRACTION Fresnel Diffraction Observatory OPTICS / FRESNEL DIFFRACTION DYNAMICS / BILLIARD Dynamical Billiard Observatory DYNAMICS / BILLIARD STOCHASTIC / ESCAPE Kramers Escape Observatory STOCHASTIC / ESCAPE

This chamber belongs to Structures & Symmetries.

STRUCTURE Back to Structures & Symmetries Route.